I do not know all the details of how Luigi works, so it's hard for me to say certain things with confidence on the basis of a few matches versus the same person, because just looking at what happens, certain things you do here may only work because the appropriate counter is not happening. (That being said you should try to play against a lot of different people, preferably better than you, that way you will avoid forming habits that do not work universally.)
Hence i will focus on things which are largely in your domain in my breakdown:
0:20 You send him flying with a forward-air, wouldn't a down-air have worked? Given the higher knock-back i would usually use down-air where possible (i.e. where there is enough time and the hit-box will reach)
0:22 If you do a fireball from the stage make sure to be closer to the edge, also given the low trajectory from the previous fair you might want to go for the edge. The lower fox recovers the smaller his range of options becomes, being on the ledge makes the illusion less viable and a fire-fox can often be intercepted with a drop-down back-air from the ledge (or if directly beneath down-air)
0:25 You hit a weak neutral-air. Firstly you unnecessarily end up in the shield and the enemy is not properly DI-ing, you could let him fall onto you and up-b (from ~80%-110%)
0:31 You jump to edge-guard with an aerial, however jumping is not the only way to do aerials, here you should have just dashed off the stage > fast fall down-air/forward-air.
0:40 Random f-smash. Can work, though risky, with fox being at 132% not necessary though. An forward-tilt probably also would have resulted in an edge-guard, and things like jab (> grab > up-throw > down-air) are often even safer pokes. Also: Angle forward-smash down vs fast-fallers, up vs floaties.
0:54 You get a up-throw turnaround d-smash, even resulting in a miss-tech but then you do the full jab-combo. Just do one jab to get a reset and free follow-ups. Here he could roll away due to the higher damage.
1:14 The double jump gets you into an unfavourable recovery position, i would try to dash and wave-dash around on enemy re-spawn or do edge-stuff.
1:19 Tournament winner. If that was on purpose: Don't do it, especially with Luigi.
1:19 You get sent flying again but should have your jump, be a bit more patient and use it, for example by recovering low with a re-jump up-air (to stop a gimp approach).
1:35 Free punish on air-dodge. You up-tilt, bad decision on that percentage, you get no guaranteed follow-ups. I would probably opt for grab > up-throw > turnaround down-smash or grab > up-throw > up-smash (may get a miss-tech)
1:49 WTF dash-attack.
2:00 Down-angled forward-tilt. Useless move, just about zero knock-back, never do it. And again, the fox was going for edge height, do something. Grab the edge if you have some time or do a run-off forward-air/down-air, if he does not do an illusion you can do fast-fall turnaround up-b to the ledge, fire-fox takes a while. (For Falco you you have to be quite careful of course as he will send you down if the illusion hits.)
2:10 Full-jump, if on purpose: Why?
2:26 Got to DI those up-throws.
3:16 Down-smash to down-smash at high percent, wonder if that is still guaranteed (given the non-existent enemy DI of course)...
3:46 Another low edge-guard situation where you should have taken the edge to prevent a safe illusion.
4:29 A short hop strong neutral-air does not necessarily yield anything at those percentages, try a full jump neutral-air to be closer to your enemy when your move is over (it usually hits people on the ground due to its 3 frame wind-up)
4:31 You hit another neutral-air. At those percentages another aerial would have given you a good edge-guard, be mindful of what your options are.
4:34 Two-stock rage-quit...
[WTF @ Next Match]
5:21 Fox gets a good DI on the down-smash for once, breaking your combo. Instead of the down-smash you could have gone for up-tilt or up-throw chains, they work quite well and lead into aerial finisher/edge-guard setups.
5:24 Another low edge-guard, which you approach with a jump, very hard to hit with aerials and in this case there was not even enough time to get to the ground fast enough.
5:29 You do a down-air when he is above you, either forward-air or up-air, both have good hit-boxes in front and above.
5:40 You get a low percent up-throw near the edge, instead of jabbing you can re-grab and do a forward-throw, which may lead to a quick gimp or at the very least a little bit better of an edge-guard.
5:47 Down-b, why here?
6:07 Re-jump to the ledge, if you have taken the fox's bad positioning into account that was all-right, if not: Try to defend yourself, up-air or fireball help keep enemies away.
6:29 Forward-throw at low percent. Not good because there is no knock-down, so you do not even get a tech-chase, up-throw instead.
6:34 Re-jump > side-b onto stage. Highly punishable, would not recommend.
6:40 Knock-down without immediate punish, would have been perfect for a jab-reset.
6:50 You are too high for that neutral-air to be pressuring enough, could have tried to simply pull out with a retreating forward-air or to hit something lower (could probably get grabbed in-between so that is not safe either)
Let's leave it at that for now, if something is unclear or if you want me to elaborate just tell me.
You are pretty fast with a lot of your follow-ups, even if they may not always be the right ones. In this match-up Fox really should get destroyed hard once he is hit, keep up the pressure if he gets too far away to continue your combo. I see a lot of room for improvement in both your edge-guard game and your recovery, which are obviously important components, check out what the top Luigis are doing in the various match-ups. Cannot say a whole lot about the neutral game, especially with Fox it's a lot of running/sliding around and poking from both sides.
